Heat equation with singular potential and singular data
Nets of Schrödinger C0-semigroups (Sε)ε with the polynomial growth with respect to ε are used for solving the Cauchy problem (∂t − Δ)U + VU = f(t, U), U(0, x) = U0(x) in a suitable generalized function algebra (or space), where V and U0 are singular generalized functions while f satisfies a Lipschit...
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| Veröffentlicht in: | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2005-08, Vol.135 (4), p.863-886 |
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| container_title | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics |
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| creator | Nedeljkov, M. Pilipović, S. Rajter-Ćirić, D. |
| description | Nets of Schrödinger C0-semigroups (Sε)ε with the polynomial growth with respect to ε are used for solving the Cauchy problem (∂t − Δ)U + VU = f(t, U), U(0, x) = U0(x) in a suitable generalized function algebra (or space), where V and U0 are singular generalized functions while f satisfies a Lipschitz-type condition. The existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates. |
| doi_str_mv | 10.1017/S0308210505000442 |
| format | Article |
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| identifier | ISSN: 0308-2105 |
| ispartof | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2005-08, Vol.135 (4), p.863-886 |
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| language | eng |
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| source | Cambridge University Press Journals Complete |
| title | Heat equation with singular potential and singular data |
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